M/M/1 is a system with poisson arrival time,
servicing exponentially and a queue of unlimited capacity and type of FIFO
Queue. This is the simplest queuing system.
NS2 supports various distributions like pareto, exponential, constant,
unifrom, etc to handle the network dynamics and metrics.
So it is very easy to test the given network
link to monitor a given queue using any of these queuing models. The listing 3 and 4 are monitoring the link when DropTail queue is used with a
capacity of finite and infinite.
Listing 13.3 uses infinite capacity and
Listing 13.4 uses Finite capacity The output screen shot is shown below the
scripts for further understanding
Listing 3 – M/M/1 Queuing Model
#new Simulator creation
set ns [new Simulator]
#trace file creation for capturing the UDP data
set tf [open out.tr w]
$ns traceall $tf
#setting the exponential distribution param
set lambda 30.0
set mu 33.0
#creation of nodes
set n1 [$ns node]
set n2 [$ns node]
#The queue limit is 1Lakh as the capacity is infinite.
Simulation will take # more time when the limit is increased.
set link [$ns simplexlink $n1 $n2 100kb 0ms DropTail]
$ns queuelimit $n1 $n2 100000
# generate random interarrival times and packet sizes
set InterArrivalTime [new RandomVariable/Exponential]
$InterArrivalTime set avg_ [expr 1/$lambda]
set pktSize [new RandomVariable/Exponential]
$pktSize set avg_ [expr 100000.0/(8*$mu)]
#create new agent UDP
set src [new Agent/UDP]
$ns attachagent $n1 $src
# queue monitoring and send the output to queue.out file
set qmon [$ns monitorqueue $n1 $n2 [open queue.out w] 0.1]
$link queuesampletimeout
proc finish {} {
global ns tf
$ns flushtrace
close $tf
exit 0
}
proc sendpacket {} {
global ns src
InterArrivalTime pktSize
set time [$ns
now]
$ns at [expr
$time + [$InterArrivalTime value]] "sendpacket"
set bytes [expr
round ([$pktSize value])]
$src send
$bytes
}
set sink [new Agent/Null]
$ns attachagent $n2 $sink
$ns connect $src $sink
$ns at 0.0001 "sendpacket"
$ns at 1000.0 "finish"
$ns run

To see the output of the above
script, execute the following in the terminal
Prompt] gawk '{ print $1, $4, $5,
$6, $7, $8, $9, $10, $11 }' queue.out > qm.pre
Prompt] xgraph qm.pre geometry
500x500 t “MM1 Queuing Example”
Here is the output screen

In the above Listing 13.3, large buffers are
used to avoid losses. One can use smaller buffers and observe losses. The way
to compute the loss probability from the simulation is simply to divide the
total number of losses by the total number of arrivals, both given in the last
line of the monitorqueue file. The command
$src set packetSize_ 100000
may be added.
The loss may be computed using the formula
P = pow(p,k)/∑Pow(p,i);
Listing 4 – M/M/1 with Finite capacity
#create new simulator
set ns [new Simulator]
#open the trace file for capturing UDP
set tf [open out.tr w]
$ns traceall $tf
#setting the parameters for Exponential distribution
set lambda 30.0
set mu 33.0
set qsize 2
set duration 2000
#creation of new nodes
set n1 [$ns node]
set n2 [$ns node]
#creation of link with queue
set link [$ns simplexlink $n1 $n2 100kb 0ms DropTail]
#setting the queue size as 2
$ns queuelimit $n1 $n2 $qsize
# generate random interarrival times and packet sizes
set InterArrivalTime [new RandomVariable/Exponential]
$InterArrivalTime set avg_ [expr 1/$lambda]
set pktSize [new RandomVariable/Exponential]
$pktSize set avg_ [expr 100000.0/(8*$mu)]
#creation of new UDP Agent
set src [new Agent/UDP]
$src set packetSize_ 100000
$ns attachagent $n1 $src
#queue monitoring
set qmon [$ns monitorqueue $n1 $n2 [open queue1.out w]
0.1]
$link queuesampletimeout
proc finish {} {
global ns tf
$ns flushtrace
close $tf
exit 0
}
proc sendpacket {} {
global ns src
InterArrivalTime pktSize
set time [$ns
now]
$ns at [expr
$time + [$InterArrivalTime value]] "sendpacket"
set bytes [expr
round ([$pktSize value])]
$src send
$bytes
}
set sink [new Agent/Null]
$ns attachagent $n2 $sink
$ns connect $src $sink
$ns at 0.0001 "sendpacket"
$ns at $duration "finish"
$ns run

To see the output of the above
script, execute the following in the terminal
Prompt] gawk '{ print $1, $4, $5,
$6, $7, $8, $9, $10, $11 }' queue1.out > qm1.pre
Prompt] xgraph qm1.pre geometry
500x500 t “MM1 Queuing Example”
Here is the output screen

Queuing models in ns2 

T S Pradeep Kumar